Question

A father and his son decides to sum their ages. The sum is equal to sixty years. Six years ago the age of the father was five times the age of the son. Six years from now the son’s age will be? ​

Answer 1

Answer:

let,

age of father be y yrs.

age of son be x yrs.

therefore,

x+y=60. eq.1

5(x-6)=(y-6)

5x-30=y-6

5x-y=-36. eq.2

By elimination method,

x=10

y=50

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Answer 2

Given :

The sum of the ages of father and son is 60 yrs .

Six years ago the age of the father was five times the age of the son.

To Find :

Age of the son after 6 years .

Solution :

$\longmapsto\tt{Let\:the\:son's\:age\:be=x}$

$\longmapsto\tt{Let\:the\:father's\:age\:be=y}$

$\longmapsto\tt{x+y=60-------(1)}$

Before 6 years :

$\longmapsto\tt{Age\:of\:son=x-6}$

$\longmapsto\tt{Age\:of\:father=y-6}$

A.T.Q :

$\longmapsto\tt{y-6=5(x-6)}$

$\longmapsto\tt{y-6=5x-30}$

$\longmapsto\tt{y=5x-30+6}$

$\longmapsto\tt\bf{y=5x-24}$

Putting the value of y in eq. (1) :

$\longmapsto\tt{x+5x-24=60}$

$\longmapsto\tt{6x-24=60}$

$\longmapsto\tt{6x=60+24}$

$\longmapsto\tt{6x=84}$

$\longmapsto\tt{x=\cancel\dfrac{84}{6}}$

$\longmapsto\tt\bf{x=14}$

Therefore :

After 6 years :

$\longmapsto\tt{Age\:of\:son=x+6}$

$\longmapsto\tt{14+6}$

$\longmapsto\tt\bf{20\:yrs}$